Detonation Characteristics of -

MORTON P. MOYLE, RICHARD B. MORRISON, and STUART W. CHURCHILL The University of Michigan, Ann Arbor, Michigan

Detonation velocities were measured in mixtures of hydrogen and oxygen containing 25 to 75 indicated by LafEtte (14)and Greene (9) % hydrogen at initial from 160' to 580'K. and initial from M to as necessary to attain stable detonation in 2 atm. The measurements were made in a number of tubes of different diameter to permit hydrogen-oxygen mixtures. The probes re- extrapolation to a tube of infinite diameter. Theoretical detonation characteristics were com- quired replacement after 20 to 30 runs. puted for the same range of conditions. The measured and computed velocities are in good The high- runs were made agreement except in rich mixtures and at subatmospheric pressures. Schlieren photographs with the coiled tube in an oven, and the reveal that the detonation wave front is very thin for a stoichiometric but degenerates low-temperature runs with the coiled tube to a complicated zone of interacting shock waves and turbulent as the percentage immersed in 5 gal. of normal propanol in of hydrogen is reduced. The detonation velocity is found to depend only slightly on initial an insulated tank. Dry was added to temperature and . The computed pressures behind the detonation and reflected waves the propanol to cool to 200°K. and are roughly proportional to initial pressure and to the reciprocal of the initial temperature. to reach lower temperatures. As the result of vigorous stirring, the tempera- The elementary theory of detonation of the elementary theory over a much ture variation within the bath was held was initiated by Riemann (21) with wider range of initial conditions. within rrfr2"K. his work on sound waves and essentially The detonation tube was evacuated and completed b Chapman (5) and Jou- EXPERIMENTAL WORK then filled with premixed oxygen and guet (7). dis elementary theory pos- The experimental equipment for the hydrogen through a mapifold and switch tulates a planar discontinuity in pres- measurement of detonation velocities con- system that kept the ignition circuit open sure, temperature, and composition sisted of six different detonation tubes, a while the filling valve was open. In the moving at sonic velocity with respect mixing and charging system, an ignition low-temperature runs the tube was evac- to the burned ases (the Chapman-Jou- system, and a timing system. uated at room temperature before cooling guet condition? ; The characteristics of the detonation to avoid condensation. In both the high- and low-temperature runs the mixture was in the burned ; no , com- tubes are given in Table 1. The five round, straight tubes (A, B, C, D, and E) were not ignited until the pressure indicated on ponent, momentum transfer to the or used to determine the effect of tube dia- a manometer had remained constant for at surroundings; and ideal behavior. meter on detonation velocity. Tube F was least 5 min. Analyses of the hydrogen and Subsequent refinements in the theory a 10-in. coil for convenience in tempera- oxygen on a spectrograph indicated have been concerned primarily with the ture control for the high- and low-tem- purities greater than 99.5%. The com- structure of the wave. The details of perature experiments. The effect of coiling position of the mixtures were regularly both the classical and the the- was evaluated by comparison of the velo- determined by the partial-pressure method oretical work are presented in modem cities measured in tubes F and B. Rec- but were periodically checked with a mass books such as Hirschfelder, Curtiss, tangular tube G was used only to obtain spectrograph. and Bird (10)and Courant and Fried- schlieren photographs. All seven tubes The schlieren measurements were made ricks (6) and therefore will not be re- were closed at both ends. by the Topler method ( 1) in a %- by The velocity of the detonation wave was %-in. rectangular tube with a test section peated herein. containing %- by 14-in. windows %-in. Experimental work on detonation has measured with ionization probes. The probes were made by drilling a no. 76 drill thick on two opposite sides. Additional been well reviewed by Lewis and von through a Teflon insert in a stainless details concerning the equipment and ex- Elbe (16),and only the immediately sleeve. The probes were threaded into perimental procedures are given in re- pertinent work will be mentioned. The the detonation tubes and adjusted so that ference 18. effect of composition on the detonation the tip was flush with the wall. Each Measurements of detonation velocity velocity of hydrogen-oxygen mixtures probe was connected as a shorting switch were repeated five or more times at the has been investigated extensively, but in the grid of an 884-thyratron tube. The same conditions to check reproducibility. the effects of initial temperature and grid bias of the thyratron tube was ad- All in all over 600 runs were carried out initial pressure have received little at- justed almost to the firing point to obtain at over 100 conditions encompassing a tention. In 1893 Dixon (7) measured maximum sensitivity. When the ionized range of compositions from 25 to 76 mole the detonation velocity in stoichiometric gases behind the detonation front reached % hydrogen for an initial temperature of 298°K. and an initial pressure of 1 atm., mixtures at 283" and over a a probe, the resistance between the probe 373°K. electrode (the drill) and ground (the a range of initial pressures from W to 2 range of pressures from 200 to 1,500 tube wall) fell, and the thyratron fired. atm. for an initial temperature of 298°K. mm. Hg. More recently Bennett and One probe and thyratron started a timer, and compositions from 40 to 76% hydro- Wedaa (2)reported detonation veloci- and another probe and thyratron stopped gen and a range of initial temperatures ties over a pressure range from 10 to it. The time interval was indicated to the from 150" to 477°K. for an initial pres- 400 mm. Hg and Hoelzer and Sto- nearest microsecond. The distances be- sure of 1 atm. and compositions from 41 baugh (11) over a range from 1 to 10 tween the probes and the distance from to 73% hydrogen. The detailed data are atm. the ignitor to the first probe are given in given in reference 18. The averages of the Lewis and Friauf (15) in 1930 and Table 1. The probe locations on tube F repeated runs are presented herein. The Berets, Greene, and Kistiakowsky (3) were on the outside of the coil and were maximum deviation of any individual velocity from the average was less than in 1950 found good agreement between determined before coiling. The distance between the probes was corrected for 1.0% except for a few runs at subatmos- velocities computed from the ele- thermal expansion and contraction of the pheric pressures. mentary theory and experimental values tube in computing the detonation velocity When the velocities measured at atmos- in hydrogen-oxygen mixtures at atmos- at nonambient temperatures. This correc- pheric pressure and 298°K. in the 0.125-, pheric pressure and near-ambient tem- tion was about 0.1% at the extreme 0.250-, 0.375-, 0.909-, and 3.250-in. peratures. The objective of this in- temperatures. The starting distance for all straight tubes were plotted as a function vestigation was to test the predictions the tubes was greater than the distance of initial , a small but

Page 92 A.1.Ch.E. Journal March, 1960 I I 0 0.250" Tube 4000 3.250" Tube 0 Payman I Walls (20) 3600 A Lewis & hiauf (15) o Berets et al. (3) - Theoretical 3200




- 1600 1I

1200 0 20 60 80 1800 40 012345678 % HYDROGEN 1 / D (inches)-' Fig. 2. Detonation velocities at and am- Fig. 1. Effect of tube diameter on detonation velocity. bient temperature. definite dependence on tube diameter was velocity is unaffected by coiling or even the National Bureau of Standards tables apparent. Therefore the velocities meas- zigzagging the tube, and the observed (23) were utilized. ured in mixtures containing 34.9, 50.0, and correction is probably due to stretching The pressure, temperature, and equi- 66.7% hydrogen were plotted vs. recipro- the tube in the coiling process rather than librium composition behind the deton- cal tube diameter in Figure 1 as suggested to fundamental effects. ation wave as well as the wave velocity by Kistiakowsky and Zinman (9). The Corrected velocities are presented in all were obtained from the computer. The data of several previous investigators (3, subsequent plots.' further increase in ressure obtained by 4, 7, 15, 20) for atmospheric pressure and temperatures near 298°K. are also in- reflection of the Betonation wave off THEORETICAL COMPUTATIONS cluded. The data appear to lie in parallel a wall was also computed with no straight lines indicating that the wall effect further change assumed in composition. The detonation characteristics of hy- The experimental velocities were not is independent of composition in this range. drogen-oxygen mixtures were computed The best set of parallel lines through the measured at exactly the same temper- data of this investigation only was deter- from the elementary theory on an IBM- atures, pressures, and compositions as mined by least squares by the use of the 650 computer over essentially the same those selected for computation. There- method of Ergun (8). These lines are range of initial temperatures, pressures, fore it was necessary to plot and inter- included in Figure 1. The slope of the and compositions as in the experimental polate the experimental data. Since the lines was computed to be 9.04 (in.) (m. )/ work. The only species assumed to be theoretical detonation velocity is a near sec.; therefore the velocities measured in present were , hydrogen, oxygen, linear function of initial pressure, tem- this and previous investigations at all con- hydroxyl, atomic hydrogen and atomic ditions were extrapolated to the perature, and composition, very little oxygen. Equilibrium constants, heat ca- uncertainty was introduced by this in- velocity in a tube of infinite diameter by pacities, and heats of formation from means of the equation terpolation. *A tabulation of the average and corrected experimental velocities and of the computed the- 9.0 oretical detonation characteristics has been fled DETONATION VELOCITIES v, =v+- as document 6124 with the American Documen- D tation Institute Photoduplication Service Liirary of Cp"gress. Washington 25, D. c., and may be The corrected experimental velocities obtamed for $1.25 photoprmts or 35-mm. micro- Data at high and low temperatures film. of this and previous investigations for were obtained only in the 0.250-in. coiled tube and on1 at atmospheric pressure. Comparison or data obtained in the coiled TABLE1. DETONATIONTUBES and straight 0.250-in. tubes at atmospheric pressure and 298°K. indicated that the Ignitor Probe coiled tube yielded velocities 1% lower separa- Total than those measured in the straight tube. to 1st I. D., in. Form probe,&. tion, ft. length, ft. Accordingly, the velocities measured in Tube Material the coiled tube at all conditions were corrected by this amount as well as by A 0.125 Straight 7.0 3.0007 11.5 Equation ( l),that is B Stainless steel 0.250 Straight 9.0 2.999 13.5 C Stainless steel 0.375 Straight 7.5 2.0003 12.0 v, 9.0 D Stainless steel 0.909 Straight 7.0 3.9944 12.0 =- v 0.99 +-D E steel 3.250 Straight 10.0 3.000 14.0 F Stainless steel 0.250 10-in. Coil 8.0 12.00 24.0 Scorah (22) maintains that the detonation G Carbon steel (0.375 x 0.5) Straight 6.0 - 7.5

Vol. 6, No. 1 A.1.Ch.E. Journal Page 93 3400

0 0 3200 z 0 5 8 hi v) v) \ \ 3000 v) v) a I +UI L $ 2800 c t U c 3 9 2600 s 5 z z 0 2400 zG za W 2 0 # 2200

1600 - 2000

1800 30 40 50 60 70 80 % HYDROGEN Fig. 5. Detonation velocities at several initial temperatures and 1 atm. Fig. 3. Detonation velocities at several initial pressures and 298' K. The effect of initial pressure on an initial pressure of 1 atm. and initial ment is demonstrated with the curve detonation velocity was investigated at temperatures of approximately 298°K. representing the computed theoretical ambient temperature only for a wide are plotted as a function of initial com- velocities over the range of composition range of compositions in the straight position in Figure 2. Excellent agree- from 20 to 80% hydrogen. 0.250- and 0.909-in. tubes. Dif6culty was encountered in obtaining reprd- ducible data at subatmospheric pres- sures in the 0.909-in. tube. Velocities Tube Dia. Theoreticol % HZ 0.250" 0.909" 76.0 A A ---- 68.0 0 40.9 0 _____-____ 40.3 V -_- 3400 --- 3000 c-- - P /---L . A" z 3200 0 8 A v) , 2800 v) 3000 E c /- - : 2800 - J ooo 0 0 2600

2400 - I I

l8O0O 0.5 1.0 1.5 2.0 2000 1 I I I I =: =: 100 200 300 400 500 PRESSURE - Atm. TEMPERATURE -OK

Fig. 4. The effect of initial pressure on detonation velocity Fig. 6. The effect of temperature on detonation velocity at at 298OK. 1 atm.

Page 94 A.1.Ch.E. Journal March, 1960 corrected to infinite diameter by Equa- TABLE2. COMPARISONOF COMPUTED ture demonstrates near proportionality. tion (1) are plotted as a function of AND EXPERIMENTALPRESSURE RATIOS Thus for a given composition the de- composition at initial pressures of 0.5, veloped pressures are roughly propor- 1.0, 1.5, and 2.0 atm. m Figure 3. The Experi- tiondto the initial . data fall somewhat below but indicate Com- mental The tem erature, pressure, and com- the same trend with pressure as the puted (19) position bekd the detonation and re- theoretical curves. The corrected ex- flected waves are extremely difficult to perimental velocities for several mix- Detonation/initid 17.5 20.4 measure because of their brief existence, tures are plotted directly vs. pressure pressure and only fragmentary experimental val- in Figure 4. This plot includes data at Reflected/detona- 2.45 3.0 ues are available for comparison with pressures intermediate to those in Fig- tion pressure the computed values. The average of ure 3. The limited range of the ordinate Reflected/initial 43.0 61.2 the detonation and reflected pressures of Figure 4 exaggerates the slight effect pressure measured by Ordin (19) for 55%hydro- of initial pressure on the detonation ve- gen at 1 atm. and 298°K. are compared with the theoretical values for the same locity and emphasizes the deviations. chemical equilibrium in a planar wave The experimental data are no more than conditions in Table 2. The agreement and neglects heat, com onent, and mo- is only fair but is probably within the 7% below the theoretical curves even mentum transfer pregcts detonation at 0.5 atm. in rich mixtures. range of uncertainty of these experi- velocities in reasonable agreement with mental values. The corrected velocities equivalent to the experimental values. those obtainable in an infinite straight The absence of firm and extensive tube are plotted as a function of gas experimental confirmation of the com- composition in Figure 5 for temper- THEORETICAL COMPOSITIONS, puted temperatures, pressures, and com- atures of 200", 300", and 477°K. Al- TEMPERATURES, AND PRESSURES ositions makes their validity uncertain though the data fall slightly below the Eut at the same time necessitates their The temperature, pressure, and equi- use for design or other engineering pur- theoretical curves, the agreement is librium composition behind the detona- generally good. The data for a number poses. The impact pressure, that is the tion wave and the pressure behind the pressure behind the reflected wave, is of mixtures are plotted directly as a reflected wave are tabulated for all the function of tem erature in Figure 6. of particular practical interest as a pos- computed conditions in reference 18 sible criterion for the design of process Again the limitel range of the ordinate and also are on file with the American exaggerates the slight variation of the equipment subject to detonation. In- Documentation Institute.* deed, Luker and Leibson (17) have re- velocity with initial temperatures and The equilibrium compostion behind emphasizes the deviations from the cently reported that the computed im- the detonation wave is illustrated in pact pressure for conditions under computed velocities which are less than Figure 8 for an initial temperature of 2.5% even in the rich mixtures. which a rupture disk just fails under 298°K. and an initial pressure of 1 detonation bears a constant ratio Schlieren photographs of detonation atm. Dissociation is observed to be sig- waves in 28.75, 39.00, and 52.50%hy- slightly greater than unity to the rated nificant for the entire range of initial static bursting pressure of the disk. drogen at ambient conditions are shown compositions. in Figure 7. The detonation wave is The detonation and reflected pressure moving from left to right in the photo- ratios are plotted as a function of initial CONCLUSIONS graphs. In Figure 7a (52.5%hydrogen) pressure for several initial compositions The detonation velocity in hydrogen- small-scale turbulence can be noted be- in Figure 9 and as a function of initial oxygen mixtures depends slightly upon hind a sharp wave front. In Figure 7b temperature for several initial composi- tube diameter. Correlation of the data (39.0%hydrogen) the wave front is tions in Figure 10. These pressure ratios for tubes of different diameter in terms thicker and the scale of the turbulence are observed to increase steeply as the of a linear relationship between veloc- is greater. In Figure 7c (28.75%hy- initial temperature decreases but to be ity and the reciprocal of the tube diam- drogen) the wave front has degenerated relatively independent of the hiitial eter as suggested by Kistiakowsky and into a complicated shock pattern fol- pressure. A plot (not shown) of the Zinman (9) emits correction of the lowed by an irregular combustion zone. pressure ratios vs. reciprocal tempera- velocities to &eir equivalent in a tube In view of these photographs, it is sur- of infinite diameter. prising that a theory which assumes * See footnote, p. 93. After this correction the experimental detonation velocities agree reasonably

z 2 1.0 v < 0.9 t $ 0.8 5 0.7 0.6 0.5 0.4 8 0.3 5 0.2 0.1 m 20 3 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 s INITIAL MOLE FRACTION OF H1 Fig. 7. Schlieren photographs of detonotion waves in hydro- Fig. 8. Equilibrium composition behind detonotion wave in gen-oxygen mixtures at otmospheric pressure ond 298'K. hydrogen-oxygen mixtures at otmospheric pressure ond 298'K. Vol. 6, No. 1 A.1.Ch.E. Journal Page 95 Mole Fraction Hz Computed Points 60 0.800 0.500 I 0.333 + Ly -. 3 u) 1 50 Ly 0 I A>I I Reflect:d-to-lnitialReflected-to-Initial Pressure Ratio I 5 h i 40 T T t-

P I I t) Dolonotion-to-Initial PIOSSUI~Ratio d 20 I I -A- E v r a I f-

INITIAL PRESSURE - Fig. 9. Effect of initial pressure on developed pressure ratios Fig. 10. Effect of initial temperature on developed pressure in hydrogen-oxygen mixtures at 298’K. ratios in hydrogen-oxygen mixtures at atmospheric pressure. well with values computed from the V = measured velocity in straight Inst. Techno]., Wright-Patterson Air elementary theory of detonation over a tube, m./sec. Force , Ohio (March, 1954). range of compositions from 20 to 80% V, = measured velocity in coiled 12. Jouguet, E., “Mbchanique des Explo- hydrogen, temperatures from 160” to tube, m./sec. sives,” 0. Doin et Fils, Paris, 477”K., and pressures from +$ to 2 V, = equivalent velocity in infinite (1917). aim. Within this range of conditions the 13. Kistiakowsky, G. B., and W. G. Zin- tube, m./sec. man, Second “Office of Naval Re- agreement between theory and experi- search Symposium on Detonation,” ment is poorest, and further investiga- LITERATURE CITED Washington, D. C. (February 9, tion is warranted for rich mixtures and 1955). subatmospheric pressures. Below 20 and 1. Beams, J. W., “Physical Measurements 14. LafEtte, P., Ann. Phys., Ser. 10, 4, above 80% hydrogen the experimental in Gas Dynamics and Combustion,” p. 587 (1925). velocities fall below the predicted val- 26, Princeton Univ. Press, Princeton, 15. Lewis, B., and J. B. Friauf, J. Amer. ues. The general agreement between New Jersey (1954). Chem. SOC., 52, 3905 (1930). theory and experimental velocities is 2. Bennett, A. L., and H. W. Wedaa, 16. Lewis, B., and G. von Elbe, “Combus- surprising in view of the significant de- Second “Office of Naval Research tion, , and of Gases,” terioration of the structure of the de- Symposium on Detonation,” Washing- Academic Press, New York (1951). tonation wave front indicated by ton, D.C. (February, 1955). 17. Luker, J. A., and M. J. Leibson, J. schlieren photographs for 39% and less 3. Berets, D. J., E. F. Greene, and G. B. Chem. Eng., 4, 133 ( 1959). 18. Moyle, M. P., Ph.D. thesis, Univ. hydrogen. Kistiakowsky, J. Amer. Chem. SOC., 72, 1080 (1950). Michigan, Ann Arbor (1956). Experimental data to test the com- 4. Campbell, C., J. Chem. SOC., 121, 2483 19. Ordin, P. M., Natl. Advkoy Comm. puted temperatures, pressures, and com- ( 1922). Aeronaut. Tech. Note 3935 (April positions are difficult to obtain and are 5. Chapman, D. L., Phil. Mag., 47, 90 1957). not generally available. However recent ( 1889). 20. Payman, W., and J. Walk, J. Chem. work indicates that the computed im- 6. Courant, R., and K. 0. Friedricks, SOC., 123, 420 (1923). pact pressure may be a suitable cri- “Supersonic Flow and Shock Waves,” 21. Riemann, B., “Ober die Fortpflanzung terion for design. Interscience Publishers, New York ebener Luftwellen von endlicher Sch- The detonation velocity depends only (1948). wingungsweite,” Abhandlungen der slightly on the initial pressure and tem- 7. Dixon, H. B., Phil. Trans. Royal SOC., Gesellschaft der Wissenschaften Zu perature but critically on the initial A184, 97 (1893). . Gottingen, Mathematisch-physikalische 8. Ergun, Sabri, Ind. Eng. Chem., 48, Klasse 8, 43 ( 1860). composition. The pressures behind the 22. Scorah, R. L., Chem. Phys., 3, 425 detonation and reflected waves depend 2063 (1956). 9. Greene, E. F., Ph.D. thesis, Harvard ( 1935). only moderately on initial composition Univ., Cambridge, Massachusetts 23. U. S National Bureau of Standards, but increase linearly with initial pres- ( 1949). “Selected Values of Chemical Thermo- sure and with the reciprocal of the ini- 10. Hirshfelder, J. F., C. F. Curtiss, and dynamic Properties,” U s. Govt. Print- tial temperature. R. B. Bird, “Molecular Theory of ing Office, Washington, D. C. (1947, Gases and ,” John Wiley, ‘New 1948). NOTATION York ( 1954). Manuscript recdued August 14, 1958; reoipion 11. Hoelzer, C.’A., and W. K. Stobaugh, received August 7 1959. aper accepted August = tube diameter, in. 18 1959. &esent&?at A.1.Ch.E. Chicago D Thesis, Air Univ. Command, USAF n;eting.

Page 96 A.1.Ch.E. Journal March, 1960